To calculate the new average amount when adding a new value to an existing dataset, you need to first determine the sum of the original data, add the new value to that sum, and then divide the result by the new total count.
Step-by-Step Calculation
Here's a breakdown of the process:
- Calculate the Original Sum: Multiply the original average by the original number of items.
- Add the New Value: Add the new amount to the original sum.
- Calculate the New Count: Increase the original number of items by 1.
- Calculate the New Average: Divide the new sum (from step 2) by the new count (from step 3).
Formula
You can express this mathematically as:
New Average = ( (Original Average * Original Count) + New Value ) / (Original Count + 1)
Example
Let's say you have an original average of 84.5 based on 4 items. You then add a new value of 100. Here's how you'd calculate the new average:
- Original Sum: 84.5 * 4 = 338
- New Sum: 338 + 100 = 438
- New Count: 4 + 1 = 5
- New Average: 438 / 5 = 87.6
Therefore, the new average is 87.6.
Summary
In essence, to find the new average, you're calculating the total value of all items (old and new) and dividing it by the total number of items. This weighted average accurately reflects the impact of the new value on the overall average.
